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用第一二项式公式进行幂运算练习

用第一二项式公式进行幂运算练习
几何画板及绘图内容加载中，请稍等……
2025-01-09 19:34
函数数列函数图像
所属专题 Binomische Formeln
该GeoGebra范例是一个交互式代数练习，用于帮助学生掌握第一二项式公式（即(a+b)²=a²+2ab+b²）的展开与计算。它通过输入框让学生输入幂的展开结果，并即时验证答案，同时提供逐步提示和反馈。核心数学概念包括二项式定理、多项式展开、代数表达式化简以及变量与系数的识别。作图要点方面，范例使用了Expand命令进行展开计算，Text和Textfield对象创建输入界面，Sequence和Join生成题目序列，If和Element实现条件判断与答案匹配，SelectedIndex和Invert用于控制选项和状态，同时通过多个列表（如ParList1、VarList1等）管理随机生成的变量和参数，dropdownSign1和dropdownSign2提供符号选择，OrderList和Order用于排序和检查。该练习适合初中7-8年级学生，用于课堂练习或家庭作业，旨在通过图形化、交互式的方式加深对二项式公式的理解和应用。

GeoGebra 命令及参数

  1. Expand(TaskFunc) → solFunc
  2. Text(inputFunc) → txtInput
  3. Sequence(Shuffle[1…3], k, 1, 100) → OrderList1, {{3, 2, 1}, {2, 3, 1}, {2, 3, 1}, {2, 3, 1}, {2, 3, 1}, {1, 2, 3}, {2, 1, 3}, {1, 2, 3}, {1, 2, 3}, {3, 1, 2}, {1, 2, 3}, {3, 2, 1}, {3, 2, 1}, {2, 3, 1}, {3, 1, 2}, {3, 1, 2}, {3, 1, 2}, {2, 1, 3}, {3, 1, 2}, {1, 3, 2}, {2, 1, 3}, {1, 2, 3}, {3, 1, 2}, {1, 2, 3}, {2, 1, 3}, {2, 3, 1}, {1, 2, 3}, {1, 3, 2}, {3, 1, 2}, {2, 1, 3}, {1, 2, 3}, {1, 2, 3}, {3, 2, 1}, {2, 1, 3}, {2, 1, 3}, {3, 1, 2}, {3, 1, 2}, {3, 2, 1}, {1, 3, 2}, {3, 1, 2}, {1, 3, 2}, {1, 3, 2}, {3, 2, 1}, {3, 1, 2}, {1, 2, 3}, {3, 1, 2}, {2, 1, 3}, {2, 3, 1}, {2, 3, 1}, {1, 3, 2}, {2, 1, 3}, {1, 3, 2}, {1, 2, 3}, {2, 1, 3}, {2, 3, 1}, {1, 2, 3}, {3, 2, 1}, {2, 3, 1}, {2, 3, 1}, {3, 1, 2}, {2, 1, 3}, {1, 3, 2}, {2, 3, 1}, {3, 2, 1}, {1, 3, 2}, {2, 3, 1}, {2, 3, 1}, {3, 2, 1}, {1, 3, 2}, {3, 2, 1}, {2, 3, 1}, {3, 2, 1}, {3, 2, 1}, {2, 3, 1}, {2, 3, 1}, {1, 3, 2}, {1, 2, 3}, {3, 1, 2}, {2, 1, 3}, {2, 3, 1}, {1, 2, 3}, {3, 2, 1}, {1, 3, 2}, {1, 2, 3}, {3, 2, 1}, {3, 1, 2}, {2, 1, 3}, {2, 1, 3}, {2, 1, 3}, {1, 2, 3}, {3, 2, 1}, {1, 3, 2}, {1, 3, 2}, {2, 1, 3}, {1, 2, 3}, {2, 3, 1}, {2, 1, 3}, {1, 2, 3}, {3, 2, 1}, {1, 3, 2}}
  4. Sequence(Shuffle[1…3], k, 1, 100) → OrderList2, {{1, 2, 3}, {2, 1, 3}, {2, 3, 1}, {3, 1, 2}, {1, 3, 2}, {1, 2, 3}, {3, 1, 2}, {2, 3, 1}, {2, 3, 1}, {2, 3, 1}, {2, 3, 1}, {2, 1, 3}, {1, 2, 3}, {1, 2, 3}, {3, 2, 1}, {2, 1, 3}, {2, 3, 1}, {1, 2, 3}, {2, 1, 3}, {2, 3, 1}, {1, 3, 2}, {2, 1, 3}, {1, 3, 2}, {1, 3, 2}, {1, 3, 2}, {2, 1, 3}, {2, 3, 1}, {1, 2, 3}, {2, 1, 3}, {3, 1, 2}, {1, 3, 2}, {3, 1, 2}, {1, 3, 2}, {2, 1, 3}, {1, 3, 2}, {3, 2, 1}, {3, 2, 1}, {1, 3, 2}, {2, 1, 3}, {3, 1, 2}, {1, 2, 3}, {1, 2, 3}, {3, 1, 2}, {1, 2, 3}, {3, 2, 1}, {1, 2, 3}, {1, 3, 2}, {2, 1, 3}, {1, 3, 2}, {3, 1, 2}, {2, 3, 1}, {2, 3, 1}, {2, 1, 3}, {2, 3, 1}, {1, 2, 3}, {3, 2, 1}, {2, 3, 1}, {1, 2, 3}, {2, 1, 3}, {2, 3, 1}, {2, 3, 1}, {3, 1, 2}, {3, 1, 2}, {2, 1, 3}, {2, 3, 1}, {2, 3, 1}, {2, 3, 1}, {1, 2, 3}, {2, 1, 3}, {1, 3, 2}, {1, 2, 3}, {1, 2, 3}, {2, 3, 1}, {3, 2, 1}, {2, 1, 3}, {3, 1, 2}, {1, 2, 3}, {1, 2, 3}, {1, 2, 3}, {1, 2, 3}, {3, 1, 2}, {1, 3, 2}, {1, 3, 2}, {1, 2, 3}, {3, 2, 1}, {3, 1, 2}, {1, 2, 3}, {3, 1, 2}, {3, 2, 1}, {3, 2, 1}, {1, 2, 3}, {3, 2, 1}, {3, 1, 2}, {3, 2, 1}, {1, 3, 2}, {3, 2, 1}, {1, 3, 2}, {1, 3, 2}, {1, 3, 2}, {3, 2, 1}}
  5. Sequence(Shuffle[1…3], k, 1, 100) → OrderList3, {{1, 2, 3}, {2, 3, 1}, {3, 1, 2}, {1, 2, 3}, {3, 1, 2}, {3, 1, 2}, {3, 2, 1}, {2, 1, 3}, {3, 2, 1}, {3, 1, 2}, {1, 3, 2}, {1, 2, 3}, {1, 2, 3}, {2, 1, 3}, {2, 3, 1}, {1, 2, 3}, {3, 1, 2}, {1, 2, 3}, {3, 2, 1}, {3, 2, 1}, {1, 2, 3}, {3, 1, 2}, {3, 1, 2}, {2, 3, 1}, {3, 2, 1}, {2, 1, 3}, {3, 2, 1}, {2, 1, 3}, {3, 1, 2}, {2, 1, 3}, {3, 1, 2}, {3, 2, 1}, {1, 3, 2}, {3, 1, 2}, {1, 3, 2}, {1, 3, 2}, {1, 2, 3}, {1, 2, 3}, {3, 1, 2}, {3, 2, 1}, {1, 2, 3}, {1, 3, 2}, {2, 1, 3}, {2, 3, 1}, {2, 3, 1}, {3, 1, 2}, {3, 2, 1}, {3, 1, 2}, {3, 1, 2}, {3, 1, 2}, {2, 1, 3}, {1, 2, 3}, {1, 3, 2}, {1, 2, 3}, {1, 2, 3}, {3, 2, 1}, {3, 2, 1}, {1, 3, 2}, {1, 3, 2}, {2, 3, 1}, {3, 2, 1}, {3, 1, 2}, {2, 1, 3}, {3, 1, 2}, {1, 3, 2}, {2, 1, 3}, {1, 3, 2}, {2, 3, 1}, {2, 1, 3}, {2, 3, 1}, {3, 1, 2}, {1, 2, 3}, {1, 2, 3}, {1, 3, 2}, {2, 1, 3}, {1, 2, 3}, {2, 3, 1}, {2, 3, 1}, {1, 3, 2}, {2, 3, 1}, {1, 2, 3}, {3, 1, 2}, {3, 1, 2}, {2, 3, 1}, {1, 3, 2}, {3, 1, 2}, {3, 2, 1}, {2, 3, 1}, {2, 3, 1}, {2, 1, 3}, {2, 1, 3}, {1, 2, 3}, {3, 2, 1}, {3, 1, 2}, {1, 2, 3}, {3, 2, 1}, {3, 2, 1}, {3, 2, 1}, {2, 3, 1}, {3, 2, 1}}
  6. Join({{"$\textsf{\phantom{144\:b² }\vphantom{gb²}}$"}, {(("$\textsf{" * DDList1(Order1(1))) * " }\vphantom{gb²}$"), (("$\textsf{" * DDList1(Order1(2))) * " }\vphantom{gb²}$"), (("$\textsf{" * DDList1(Order1(3))) * "\vphantom{gb²}}$")}}) → dropdown1
  7. Join({{"$\textsf{\phantom{144\:b² }\vphantom{gb²}}$"}, {(("$\textsf{" * DDList3(Order3(1))) * " }\vphantom{gb²}$"), (("$\textsf{" * DDList3(Order3(2))) * " }\vphantom{gb²}$"), (("$\textsf{" * DDList3(Order3(3))) * "\vphantom{gb²}}$")}}) → dropdown3
  8. Join({{"$\textsf{\phantom{144\:b² }\vphantom{gb²}}$"}, {(("$\textsf{" * DDList2(Order2(1))) * " }\vphantom{gb²}$"), (("$\textsf{" * DDList2(Order2(2))) * " }\vphantom{gb²}$"), (("$\textsf{" * DDList2(Order2(3))) * "\vphantom{gb²}}$")}}) → dropdown2
  9. SelectedIndex(dropdown1) → indexdd1
  10. SelectedIndex(dropdown2) → indexdd2
  11. SelectedIndex(dropdown3) → indexdd3
  12. SelectedIndex(dropdownSign1) → indexddS1
  13. SelectedIndex(dropdownSign2) → indexddS2
  14. If(Case ≠ 3, indexdd2 - 1 ≟ IndexOf[1, Order2], true) → correctdd2
  15. If(Case ≠ 3, indexddS2 ≟ 2, true) → correctddS2
  16. If(step ≟ 1, correctExtend ∧ correctValue, correctdd1 ∧ correctdd2 ∧ correctdd3 ∧ correctddS1 ∧ correctddS2) → correct
  17. Sequence(Random[1, 10], i, 1, 10) → randomNumbers, {2, 4, 6, 6, 8, 3, 2, 7, 9, 1}
  18. Element(randomNumbers, Mod[questionCount, Length[randomNumbers]] + 1) → randomNumber
  19. If(step ≟ 1, Defined[inputFunc], indexdd1 ≠ 1 ∧ If[Case ≟ 3, true, indexdd2 ≠ 1] ∧ indexdd3 ≠ 1 ∧ indexddS1 ≠ 1 ∧ If[Case ≟ 3, true, indexddS2 ≠ 1]) → clickableBtnValidate
  20. Textfield(inputFunc) → inputBox
  21. If(CaseVar ≟ 2, "", var1) → txtVar1
  22. If(CaseVar ≟ 1, "", var2) → txtVar2
  23. Invert(pixMat) → invPixMat
  24. If(Case ≟ 3, PosDDS1 + (1.42, 0), PosDDS2 + (1.42, 0)) → PosDD3

AI 绘图提示语参考

这是一个交互式代数练习界面，用于帮助学生掌握二项式公式。界面包含一个文本输入框，学生可以输入展开后的代数式；下方显示一个随机生成的二项式问题，如(a+b)^2；旁边有验证反馈区域，当输入正确时会显示确认信息。界面还包含符号选择下拉菜单和排序选项，用于控制问题生成和验证逻辑。构造顺序为：先创建输入框和问题显示区域，然后通过随机列表生成问题，接着添加验证条件，最后调整界面布局以实现交互功能。
以上提示语为根据原始绘图命令整理而来，仅供参考。